to support any number of phases

correction in MovingPhaseModel<BasePhaseModel>::correct()

to correspond to the phase dilatation rate.

to support any number of phases

Multi-species, mass-transfer and reaction support and multi-phase
structure provided by William Bainbridge.

Integration of the latest p-U and face-p_U algorithms with William's
multi-phase structure is not quite complete due to design
incompatibilities which needs further development.  However the
integration of the functionality is complete.

The results of the tutorials are not exactly the same for the
twoPhaseEulerFoam and reactingTwoPhaseEulerFoam solvers but are very
similar.  Further analysis in needed to ensure these differences are
physical or to resolve them; in the meantime the twoPhaseEulerFoam
solver will be maintained.

This is necessary to guarantee consistency between the residualAlpha
used for drag and buoyancy in a multi-phase system

twoPhaseEulerFoam: Update only the fixed-value phi patch fields before constructing the pressure eqn
Avoids small continuity error in parallel

twoPhaseEulerFoam: In the limit of phase-fraction->0 the velocity is calculated from a force balance

Rather than forcing the dispersed-phase velocity -> the continuous-phase
velocity as the phase-fraction -> 0 the velocity is now calculated from
a balance of pressure, buoyancy and drag forces.  The advantage is now
liquid or particles are not carried out of bubble-column of
fluidised-beds by the fictitious drag caused by forcing the
phase-velocities becoming equal in the limit.

This formulation provides C-grid like pressure-flux staggering on an
unstructured mesh which is hugely beneficial for Euler-Euler multiphase
equations as it allows for all forces to be treated in a consistent
manner on the cell-faces which provides better balance, stability and
accuracy.  However, to achieve face-force consistency the momentum
transport terms must be interpolated to the faces reducing accuracy of
this part of the system but this is offset by the increase in accuracy
of the force-balance.

Currently it is not clear if this face-based momentum equation
formulation is preferable for all Euler-Euler simulations so I have
included it on a switch to allow evaluation and comparison with the
previous cell-based formulation.  To try the new algorithm simply switch
it on, e.g.:

PIMPLE
{
    nOuterCorrectors 3;
    nCorrectors      1;
    nNonOrthogonalCorrectors 0;
    faceMomentum     yes;
}

It is proving particularly good for bubbly flows, eliminating the
staggering patterns often seen in the air velocity field with the
previous algorithm, removing other spurious numerical artifacts in the
velocity fields and improving stability and allowing larger time-steps
For particle-gas flows the advantage is noticeable but not nearly as
pronounced as in the bubbly flow cases.

Please test the new algorithm on your cases and provide feedback.

Henry G. Weller
CFD Direct

Updated tutorials to converge pressure during PIMPLE loop to avoid
phase-fraction unboundedness which limits thermodynamics convergence.

Reduces or eliminates staggering patterns due to cell-force imbalances
Resolves bug-report http://www.openfoam.org/mantisbt/view.php?id=1363

Improves stability and convergence of systems in which drag dominates
e.g. small particles in high-speed gas flow.

Additionally a new ddtPhiCorr strategy is included in which correction
is applied only where the phases are nearly pure.  This reduces
staggering patters near the free-surface of bubble-column simulations.